Abstract

The most frequency-stable sources of electromagnetic radiation are produced optically, and optical frequency combs provide the means for high-fidelity frequency transfer across hundreds of terahertz and into the microwave domain. A critical step in this photonic-based synthesis of microwave signals is the optical-to-electrical conversion process. Here, we show that attosecond (as) timing stability can be preserved across the opto-electronic interface of a photodiode, despite an intrinsic temporal response that is more than six orders of magnitude slower. The excess timing noise in the photodetection of a periodic train of ultrashort optical pulses behaves as flicker noise (1/f) with amplitude of 4as/Hz at 1 Hz offset. The corresponding fractional frequency fluctuations are 1.4×1017 at 1 s and 5.5×1020 at 1000 s. These results demonstrate that direct photodetection, as part of frequency-comb-based microwave synthesis, can support the timing performance of the best optical frequency standards, and thereby opens the possibility for generating microwave signals with significantly better stability than any existing source.

© 2015 Optical Society of America

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    [Crossref]

2014 (5)

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506, 71–75 (2014).
[Crossref]

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref]

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10(-18) level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113, 203901 (2014).

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. G. Zhou, A. Cross, J. C. Campbell, S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39, 1581–1584 (2014).
[Crossref]

2013 (5)

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[Crossref]

M. Lessing, H. S. Margolis, C. T. A. Brown, P. Gill, G. Marra, “Suppression of amplitude-to-phase noise conversion in balanced optical-microwave phase detectors,” Opt. Express 21, 27057–27062 (2013).
[Crossref]

K. Jung, J. Shin, J. Kim, “Ultralow phase noise microwave generation from mode-locked Er-fiber lasers with subfemtosecond integrated timing jitter,” IEEE Photon. J. 5, 5500906 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38, 1712–1714 (2013).
[Crossref]

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
[Crossref]

2012 (6)

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, J. Ye, “A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity,” Nat. Photonics 6, 687–692 (2012).
[Crossref]

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

J. G. Hartnett, N. R. Nand, C. Lu, “Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators,” Appl. Phys. Lett. 100, 183501 (2012).
[Crossref]

K. Jung, J. Kim, “Subfemtosecond synchronization of microwave oscillators with mode-locked Er-fiber lasers,” Opt. Lett. 37, 2958–2960 (2012).
[Crossref]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

A. J. Benedick, J. G. Fujimoto, F. X. Kartner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6, 97–100 (2012).
[Crossref]

2011 (6)

F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
[Crossref]

Z. Li, Y. Fu, M. Piels, H. P. Pan, A. Beling, J. E. Bowers, J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385–B390 (2011).
[Crossref]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[Crossref]

J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
[Crossref]

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

2010 (1)

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
[Crossref]

2009 (2)

D. Meiser, J. Ye, D. R. Carlson, M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102, 163601 (2009).
[Crossref]

E. N. Ivanov, M. E. Tobar, “Low phase-noise sapphire crystal microwave oscillators: current status,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 263–269 (2009).
[Crossref]

2008 (1)

J. Kim, J. A. Cox, J. Chen, F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics 2, 733–736 (2008).
[Crossref]

2007 (1)

E. N. Ivanov, J. J. McFerran, S. A. Diddams, L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736–745 (2007).
[Crossref]

2006 (2)

E. Rubiola, E. Salik, N. Yu, L. Maleki, “Flicker noise in high speed p-i-n photodiodes,” IEEE Trans. Microwave Theor. Tech. 54, 816–820 (2006).
[Crossref]

J. F. Cliche, B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Control Syst. 26, 19–26 (2006).
[Crossref]

2005 (3)

E. N. Ivanov, S. A. Diddams, L. Hollberg, “Study of the excess noise associated with demodulation of ultra-short infrared pulses,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 1068–1074 (2005).
[Crossref]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, L. Hollberg, “Low noise synthesis of microwave signals from an optical source,” IEEE Electron Device Lett. 41, 650–651 (2005).
[Crossref]

W. Shieh, L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474–476 (2005).
[Crossref]

2004 (2)

J. Kim, F. X. Kartner, M. H. Perrott, “Femtosecond synchronization of radio frequency signals with optical pulse trains,” Opt. Lett. 29, 2076–2078 (2004).
[Crossref]

L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
[Crossref]

1999 (1)

G. Santarelli, P. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, C. Salomon, “Quantum projection noise in an atomic fountain: a high stability cesium frequency standard,” Phys. Rev. Lett. 82, 4619–4622 (1999).
[Crossref]

1993 (1)

A. M. Joshi, G. H. Olsen, V. S. Ban, E. Mykietyn, M. J. Lange, D. T. Mohr, “Reduction of 1/F noise in multiplexed linear In0.53Ga0.47As detector arrays via epitaxial doping,” IEEE Trans. Electron Devices 40, 303–308 (1993).
[Crossref]

1988 (1)

M. B. Weissman, “1/F noise and other slow, nonexponential kinetics in condensed matter,” Rev. Mod. Phys. 60, 537–571 (1988).
[Crossref]

Argence, B.

D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10(-18) level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

Ban, V. S.

A. M. Joshi, G. H. Olsen, V. S. Ban, E. Mykietyn, M. J. Lange, D. T. Mohr, “Reduction of 1/F noise in multiplexed linear In0.53Ga0.47As detector arrays via epitaxial doping,” IEEE Trans. Electron Devices 40, 303–308 (1993).
[Crossref]

Bartels, A.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, L. Hollberg, “Low noise synthesis of microwave signals from an optical source,” IEEE Electron Device Lett. 41, 650–651 (2005).
[Crossref]

L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
[Crossref]

Baynes, F. N.

Beling, A.

Beloy, K.

N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
[Crossref]

Benedick, A. J.

A. J. Benedick, J. G. Fujimoto, F. X. Kartner, “Optical flywheels with attosecond jitter,” Nat. Photonics 6, 97–100 (2012).
[Crossref]

Bergquist, J. C.

T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
[Crossref]

Berizzi, F.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref]

Bi, Z. Y.

L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
[Crossref]

Bishof, M.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506, 71–75 (2014).
[Crossref]

Bloom, B. J.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506, 71–75 (2014).
[Crossref]

Bogoni, A.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
[Crossref]

Boudot, R.

W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
[Crossref]

Bowers, J. E.

Bromley, S. L.

B. J. Bloom, T. L. Nicholson, J. R. Williams, S. L. Campbell, M. Bishof, X. Zhang, W. Zhang, S. L. Bromley, J. Ye, “An optical lattice clock with accuracy and stability at the 10(-18) level,” Nature 506, 71–75 (2014).
[Crossref]

Brown, C. T. A.

Campbell, J.

Campbell, J. C.

W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113, 203901 (2014).

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. G. Zhou, A. Cross, J. C. Campbell, S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39, 1581–1584 (2014).
[Crossref]

F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[Crossref]

Z. Li, Y. Fu, M. Piels, H. P. Pan, A. Beling, J. E. Bowers, J. C. Campbell, “High-power high-linearity flip-chip bonded modified uni-traveling carrier photodiode,” Opt. Express 19, B385–B390 (2011).
[Crossref]

Campbell, S. L.

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W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
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A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
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Li, Z.

Lours, M.

W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
[Crossref]

A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
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W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
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J. G. Hartnett, N. R. Nand, C. Lu, “Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators,” Appl. Phys. Lett. 100, 183501 (2012).
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T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
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F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
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Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
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A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Le Coq, G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36, 3654–3656 (2011).
[Crossref]

G. Santarelli, P. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, C. Salomon, “Quantum projection noise in an atomic fountain: a high stability cesium frequency standard,” Phys. Rev. Lett. 82, 4619–4622 (1999).
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Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
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L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
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E. Rubiola, E. Salik, N. Yu, L. Maleki, “Flicker noise in high speed p-i-n photodiodes,” IEEE Trans. Microwave Theor. Tech. 54, 816–820 (2006).
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W. Shieh, L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474–476 (2005).
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G. Santarelli, P. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, C. Salomon, “Quantum projection noise in an atomic fountain: a high stability cesium frequency standard,” Phys. Rev. Lett. 82, 4619–4622 (1999).
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Marra, G.

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T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, J. Ye, “A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity,” Nat. Photonics 6, 687–692 (2012).
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E. N. Ivanov, J. J. McFerran, S. A. Diddams, L. Hollberg, “Noise properties of microwave signals synthesized with femtosecond lasers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 736–745 (2007).
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A. M. Joshi, G. H. Olsen, V. S. Ban, E. Mykietyn, M. J. Lange, D. T. Mohr, “Reduction of 1/F noise in multiplexed linear In0.53Ga0.47As detector arrays via epitaxial doping,” IEEE Trans. Electron Devices 40, 303–308 (1993).
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J. G. Hartnett, N. R. Nand, C. Lu, “Ultra-low-phase-noise cryocooled microwave dielectric-sapphire-resonator oscillators,” Appl. Phys. Lett. 100, 183501 (2012).
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T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38, 1712–1714 (2013).
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T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
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L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
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T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
[Crossref]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L. S. Ma, C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
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J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, L. Hollberg, “Low noise synthesis of microwave signals from an optical source,” IEEE Electron Device Lett. 41, 650–651 (2005).
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A. M. Joshi, G. H. Olsen, V. S. Ban, E. Mykietyn, M. J. Lange, D. T. Mohr, “Reduction of 1/F noise in multiplexed linear In0.53Ga0.47As detector arrays via epitaxial doping,” IEEE Trans. Electron Devices 40, 303–308 (1993).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
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Pinna, S.

P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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W. Sun, F. Quinlan, T. M. Fortier, J. D. Deschenes, Y. Fu, S. A. Diddams, J. C. Campbell, “Broadband noise limit in the photodetection of ultralow jitter optical pulses,” Phys. Rev. Lett. 113, 203901 (2014).

F. Quinlan, F. N. Baynes, T. M. Fortier, Q. G. Zhou, A. Cross, J. C. Campbell, S. A. Diddams, “Optical amplification and pulse interleaving for low-noise photonic microwave generation,” Opt. Lett. 39, 1581–1584 (2014).
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F. Quinlan, T. M. Fortier, H. Jiang, A. Hati, C. Nelson, Y. Fu, J. C. Campbell, S. A. Diddams, “Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trains,” Nat. Photonics 7, 290–293 (2013).
[Crossref]

T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38, 1712–1714 (2013).
[Crossref]

T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
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F. Quinlan, T. M. Fortier, M. S. Kirchner, J. A. Taylor, M. J. Thorpe, N. Lemke, A. D. Ludlow, Y. Y. Jiang, S. A. Diddams, “Ultralow phase noise microwave generation with an Er:fiber-based optical frequency divider,” Opt. Lett. 36, 3260–3262 (2011).
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J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
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T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, J. Ye, “A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity,” Nat. Photonics 6, 687–692 (2012).
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L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
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T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
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T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5, 425–429 (2011).
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E. Rubiola, E. Salik, N. Yu, L. Maleki, “Flicker noise in high speed p-i-n photodiodes,” IEEE Trans. Microwave Theor. Tech. 54, 816–820 (2006).
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E. Rubiola, E. Salik, N. Yu, L. Maleki, “Flicker noise in high speed p-i-n photodiodes,” IEEE Trans. Microwave Theor. Tech. 54, 816–820 (2006).
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D. Nicolodi, B. Argence, W. Zhang, R. Le Targat, G. Santarelli, Y. Le Coq, “Spectral purity transfer between optical wavelengths at the 10(-18) level,” Nat. Photonics 8, 219–223 (2014).
[Crossref]

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G. Santarelli, P. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, C. Salomon, “Quantum projection noise in an atomic fountain: a high stability cesium frequency standard,” Phys. Rev. Lett. 82, 4619–4622 (1999).
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P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507, 341–345 (2014).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
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W. Zhang, T. Li, M. Lours, S. Seidelin, G. Santarelli, Y. Le Coq, “Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation,” Appl. Phys. B 106, 301–308 (2012).
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N. Hinkley, J. A. Sherman, N. B. Phillips, M. Schioppo, N. D. Lemke, K. Beloy, M. Pizzocaro, C. W. Oates, A. D. Ludlow, “An atomic clock with 10(-18) instability,” Science 341, 1215–1218 (2013).
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W. Shieh, L. Maleki, “Phase noise characterization by carrier suppression techniques in RF photonic systems,” IEEE Photon. Technol. Lett. 17, 474–476 (2005).
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T. M. Fortier, C. W. Nelson, A. Hati, F. Quinlan, J. Taylor, H. Jiang, C. W. Chou, T. Rosenband, N. Lemke, A. Ludlow, D. Howe, C. W. Oates, S. A. Diddams, “Sub-femtosecond absolute timing jitter with a 10  GHz hybrid photonic-microwave oscillator,” Appl. Phys. Lett. 100, 231111 (2012).
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J. Taylor, S. Datta, A. Hati, C. Nelson, F. Quinlan, A. Joshi, S. Diddams, “Characterization of power-to-phase conversion in high-speed P-I-N photodiodes,” IEEE Photon. J. 3, 140–151 (2011).
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J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, L. Hollberg, “Low noise synthesis of microwave signals from an optical source,” IEEE Electron Device Lett. 41, 650–651 (2005).
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L. S. Ma, Z. Y. Bi, A. Bartels, L. Robertsson, M. Zucco, R. S. Windeler, G. Wilpers, C. Oates, L. Hollberg, S. A. Diddams, “Optical frequency synthesis and comparison with uncertainty at the 10(-19) level,” Science 303, 1843–1845 (2004).
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W. Zhang, Z. Xu, M. Lours, R. Boudot, Y. Kersale, G. Santarelli, Y. Le Coq, “Sub-100 attoseconds stability optics-to-microwave synchronization,” Appl. Phys. Lett. 96, 211105 (2010).
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Appl. Phys. B (1)

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Figures (6)

Fig. 1.
Fig. 1. Conceptual diagram of optical frequency division illustrating the different timescales for the optical and microwave signals. (a) An ultrastable CW optical frequency reference, such as an optical cavity or an optical atomic clock, provides the intrinsic timing stability at and below the intrinsic femtosecond scale of the optical carrier wave [14]. (b) The optical timing stability is transferred to an optical frequency comb that provides a coherent link to the microwave-rate optical pulse train that consists of subpicosecond pulses [10,11]. (c) Photodetection of the optical pulse train results in electrical pulses on the 10 ps timescale from which a 10 GHz microwave signal is obtained. In this work we explore the noise limitations of this optical-to-electrical conversion process and show that timing can be preserved down to the attosecond (as) level. As indicated in the expanded view of (d), this implies a time-averaged splitting of the 100 ps period of the photonically generated microwaves by more than a factor of 107.
Fig. 2.
Fig. 2. Measuring optical-to-microwave conversion noise with the carrier suppression technique. MLL, mode-locked laser; interleaver used as a repetition rate multiplier; EDFA, erbium-doped fiber optical amplifier; AOM, acousto-optic modulator; α, variable attenuator; ϕ, variable phase shifter; ADC, analog-to-digital converter; FFT, Fourier transform spectrum analyzer; BP, band pass filter; LPF, low pass filter.
Fig. 3.
Fig. 3. Excess phase and timing noise spectrum for the generation of a 10 GHz microwave signal from direct photodetection. The solid black line is flicker noise of 135dBc/Hz, and the lower green curve is the measurement noise floor. For comparison, the red dashed lines are the projected phase noise of ultrastable CW lasers (divided to 10 GHz) having combined flicker and white frequency noise floors equivalent to fractional frequency stability of 5×1016 and 5×1017 at 1 s, respectively.
Fig. 4.
Fig. 4. (Top) Residual timing error in the optical-to-microwave conversion process for two MUTC photodiodes. The RMS variation over 6000 s of measurement is less than 106 as in a measurement bandwidth of 10 Hz. (Bottom) Timing deviation for a single MUTC photodiode for a 10 GHz carrier.
Fig. 5.
Fig. 5. Fractional frequency stability of the excess noise in direct photodetection leading to a 10 GHz microwave signal (10 Hz measurement bandwidth). The dashed lines represent (a) stability of a cryogenic sapphire microwave oscillator [22], (b) neutral atom lattice clock [3,4], (c) projected thermal noise floor of an optical silicon Fabry–Perot cavity [1], and (d) residual noise of an optical frequency comb [10]. Also shown are the projected flicker noise of 135dBc/Hz and the measurement noise floor.
Fig. 6.
Fig. 6. AM-to-PM coefficient of the two MUTC photodiodes used in this work expressed as the suppression of RIN converted to single sideband phase noise. Bias voltages of 18V (blue curve) and 12V (red curve) were chosen for the two different photodiodes to provide an AM-to-PM null at 24 mA of photocurrent.

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